The second model that we will employ describes a non-Hermitian Floquet
second-order topological insulator (FSOTI), which could possess multiple
quartets of corner-localized states at real quasienergies zero and
\(\pi \)  [1]}. The Hamiltonian of the model takes the form
of \(H(t)={\cal H}_{1}\)  for \(t\in [\ell +1/2,\ell +1)\)  and \(H(t)={\cal H}_{2}\) 
for \(t\in [\ell ,\ell +1/2)\)  with \(\ell \in \mathbb {Z}\) . Here
\({\cal H}_{1(2)}={\cal H}_{x}\otimes \mathbb {I}_{y}+\mathbb {I}_{x}\otimes {\cal H}_{y1(y2)},\) 
\({\cal H}_{x}=\Delta \sum _{m,n}(|m,n\rangle \langle m+1,n|\otimes \sigma _{-}+{\rm H.c.}),\) 
\({\cal H}_{y1}=\sum _{m,n}(iJ_{2}|m,n+1\rangle \langle m,n|+{\rm H.c.}+2\mu |m,n\rangle \langle m,n|)\otimes \sigma _{z},\) 
\({\cal H}_{y2}=J_{1}\sum _{m,n}(|m,n\rangle \langle m,n+1|+{\rm H.c.})\otimes \sigma _{x}.\) 
